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10 votes
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Quadrilateral OPQR is inscribed in circle N, as shown below. What is the measure of ∠QRO? (5 points)

Quadrilateral OPQR is inscribed in circle N. Angle O is labeled x plus 17 degrees, angle Q is 6x minus 5 degrees, and angle R i

41
67
113
139

Quadrilateral OPQR is inscribed in circle N, as shown below. What is the measure of-example-1
User Anar
by
2.5k points

1 Answer

9 votes
9 votes

Opposite angles of a cyclic quadrilateral are supplementary, so


x+17+6x-5=180 \\ \\ 7x+12=180 \\ \\ 7x=168 \\ \\ x=24 \\ \\ \\ \implies \angle QRO=2(24)+19=\boxed{67^(\circ)}

User Dolly Aswin
by
2.9k points
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